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feat: Fermat's last theorem test #1789
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,79 @@ | ||
| /* | ||
| * Fermat's Last Theorem states: | ||
| * | ||
| * For every integer n >= 3, the equation | ||
| * | ||
| * x^n + y^n = z^n | ||
| * | ||
| * has no nontrivial integer solutions (x, y, z > 0). | ||
| * | ||
| * In contrast, for n = 2 there are infinitely many solutions (the famous | ||
| * Pythagorean triples like 3^2 + 4^2 = 5^2). | ||
| * | ||
| * While Andrew Wiles proved this theorem in 1994 using advanced mathematics | ||
| * (elliptic curves and modular forms), we can illustrate the theorem in JavaScript | ||
| * by brute-force checking ranges of x, y, z for small exponents n. | ||
| * | ||
| * within checked ranges, no counterexamples exist for n >= 3. | ||
| */ | ||
|
|
||
| /** | ||
| * Check for counterexamples to Fermat's Last Theorem within a bounded range. | ||
| * | ||
| * This function uses BigInt arithmetic to handle large ranges safely. | ||
| * | ||
| * @param {number} maxValue - The maximum integer to check for x and y | ||
| * @param {number} exponent - The power n (>= 3) | ||
| * @returns {Array} - Array of counterexamples found (should be empty) | ||
| */ | ||
|
|
||
| const checkFermatLastTheorem = (maxValue, exponent) => { | ||
| if (exponent < 3) { | ||
| throw new Error("Fermat's Last Theorem only applies for n >= 3") | ||
| } | ||
|
|
||
| const counterexamples = [] | ||
| const exponentBigInt = BigInt(exponent) | ||
|
|
||
| for (let baseX = 1; baseX <= maxValue; baseX++) { | ||
| const baseXPowerN = BigInt(baseX) ** exponentBigInt | ||
|
|
||
| for (let baseY = baseX; baseY <= maxValue; baseY++) { | ||
| const baseYPowerN = BigInt(baseY) ** exponentBigInt | ||
| const sumOfPowers = baseXPowerN + baseYPowerN | ||
|
|
||
| // compute integer nth root of sumOfPowers using binary search | ||
| let lowerBound = 1n | ||
| let upperBound = sumOfPowers | ||
| let potentialZ = 0n | ||
|
|
||
| while (lowerBound <= upperBound) { | ||
| const middle = (lowerBound + upperBound) >> 1n | ||
| const middlePowerN = middle ** exponentBigInt | ||
|
|
||
| if (middlePowerN === sumOfPowers) { | ||
| potentialZ = middle | ||
| break | ||
| } else if (middlePowerN < sumOfPowers) { | ||
| lowerBound = middle + 1n | ||
| } else { | ||
| upperBound = middle - 1n | ||
| } | ||
| } | ||
|
|
||
| // exact check | ||
| if (potentialZ > 0n && potentialZ ** exponentBigInt === sumOfPowers) { | ||
| counterexamples.push({ | ||
| x: baseX, | ||
| y: baseY, | ||
| z: potentialZ.toString(), | ||
| n: exponent | ||
| }) | ||
| } | ||
| } | ||
| } | ||
|
|
||
| return counterexamples | ||
| } | ||
|
|
||
| export default checkFermatLastTheorem |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,30 @@ | ||
| import checkFermatLastTheorem from '../FermatsLastTheoremTest.js' | ||
|
|
||
| describe("Fermat's Last Theorem Checker (BigInt version)", () => { | ||
| test('throws an error if exponent is less than 3', () => { | ||
| expect(() => checkFermatLastTheorem(10, 2)).toThrow( | ||
| "Fermat's Last Theorem only applies for n >= 3" | ||
| ) | ||
| expect(() => checkFermatLastTheorem(10, 1)).toThrow() | ||
| }) | ||
|
|
||
| test('small range test: returns empty array for n = 3, max 20', () => { | ||
| const results = checkFermatLastTheorem(20, 3) | ||
| expect(results).toEqual([]) | ||
| }) | ||
|
|
||
| test('moderate range test: returns empty array for n = 3, max 1000', () => { | ||
| const results = checkFermatLastTheorem(1000, 3) | ||
| expect(results).toEqual([]) | ||
| }) | ||
|
|
||
| test('small range test: returns empty array for n = 4, max 20', () => { | ||
| const results = checkFermatLastTheorem(20, 4) | ||
| expect(results).toEqual([]) | ||
| }) | ||
|
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||
| test('moderate range test: returns empty array for n = 4, max 500', () => { | ||
| const results = checkFermatLastTheorem(500, 4) | ||
| expect(results).toEqual([]) | ||
| }) | ||
| }) |
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